Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y = e4x cos 2x y" - 8y' + 20y = 0; When y = e4x cos 2x, y' = y" = Thus, in terms of x, y"8y' + 20y = + 20 e4x cos 2x

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
y" - 8y' + 20y = 0; y = e4x cos 2x
When y=e4x cos 2x,
y' =
y" =
Thus, in terms of x,
y" - 8y' + 20y =
+ 20e4x cos 2x
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" - 8y' + 20y = 0; y = e4x cos 2x When y=e4x cos 2x, y' = y" = Thus, in terms of x, y" - 8y' + 20y = + 20e4x cos 2x
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